i!iu’’mnm lunbobt · i!iu’’mnm lunbobt originally issued i july1945 as advtxnce...

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NATION_AL ADVISORY COMMITTEE FOR AERONAUTICS

I!iu’’mnm lUNBOBTORIGINALLY ISSUED I

July 1945 asAdvtxnce RestrictedReportL5F27a

AllANALYSISOF

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LIFE EKPECTJW3XOF AIRPLANEUTNGS

NORMALCRTJISDiGFLCG3T

By AbbottA. Putnam

LangleyMamrial AeronauticalLaboratoryLangleyField,Va.

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WASHINGTON

NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the war effort. They were pre-viously held under a security status but are now unclassified. Some of these reports were not tech-nically edited. All have been reproduced without change in order to expedite general distribution.

https://ntrs.nasa.gov/search.jsp?R=19930093588 2020-07-26T16:54:03+00:00Z

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1

NACA ARR No. L5F27a ~

NATIONAL ADVISORY COMMITTEE

ADVANCE RESTRICT.~..... ...... .

AN ANALYSIS OF IJFE EXPECTANCY

. .- —

FOR AERONAUTICS

.~PORT -----

OF AIRPLANE WINGS

IN NORMAL CRUISING FLIGH17

By Abbott A. Putnam

SUMMARY

In order to provide a basis for judging the relativeImportance of wing failure by fatigue and by singleintense gusts, an analysis of wing life for normalcruising f13.ghtwas made based on data on the frequencyof atmospheric gusta. The independent variables con-sidered in the analysis included stress-concentrationfactor, stress-load relation, wing loading, design andcrulshg speeds, design gust velocity, and airplane size.Several methods for estimating fatigue life from gustfrequencies are discussed. The procedure selected forthe analysis is believed to be simple and reasonablyaccurate, though slightly conservative.

The results of the analysis indicate that, In gen-eral, the fatigue life and single-gust life of an air-plane wing are of about equal tiportance for conventionaldesigns and normal operating renditions. The fatiguelife appears to be influenced mainly by the detail designand construction and not greatly by normal changes inoperating speed or by moderate changes in the design gustvelocity. Single-gust life, however, is not appreciablyaffected by the detail design and construction but ismarkedly affected by operating speed and by changes indesign gust velocity. The trends in design toward higherwing loading, reduced load factor, larger size, andincreased speed appear to have a small effect on bothfatigue life and single-gust life.

INTRODUCTION

Considerable interest has recently developed in thiscountry concerning the fatigue life expectancy of theprimary structure of an airplane. The trends in airplane .

2 .NACA A.RRNo. L5F27a

design toward higher speed, higher wing loading, andlarger size have been cited as indications that fatiguetroubles and reduced life are becoming of increasingimportance. Available literature does not show veryclearly, however, whether fatigue life is important.Authentic cases of fatigue failure of the primary struc-ture have not been cited. Furthermore, no evidence hasbeen presented for assuming that design trends shortenfatigue life. The obscurity of this subject is partlythe result of the absence of statistical data on therepeated loads or stresses to which airplane structuresmay be subjected in service operations and the consequentabsence of analytical treatments of the problem.

In order to estimate the relative importance offatigue in the primary structure, an analysis is madeherein of the effects of a number of variables on thefatigue life of airplane wing structures subjected to thenumerous gusts encountered in normal transport flightoperations. For this purpose, the statistical gust dataof reference 1 have been utilized. The values of fatiguellfe thus obtained are compared with the life expectancybased on the probability of encountering single gusts ofexcessive magnitude.

Inmost of the cases analyzed, it is assumed thatthe wing is designed to withstand a static load corre-sponding to the load imposed by a gust having a velocityof 30 feet per second at design level-flight speed. Forthis condition the effects of stress-concentration factor,fatigue properties of the structural material, designspeed, desi~ wing loadlng, and stress-load relation weredetermined. The effects of variation of the design loadcondition are also determined and the effect of airplanesize is considered.

METHOD OF ANALYSIS

Single-Gust Life

As pointed out in reference 1, ‘lLii?eexpectancy isgoverned not only by fatigue but also by the probabilityof occurrence of single quasi-static loads of such highmagnitude as might endanger the structure directly.if Theprobable life, as governed by the action of a singleexcessive gust, may be termed the “single-gust lifetfand

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NACA ARR No. L5F27a 3

Is taken herein as the number of miles required, on theaverage, to encounter a gust suf’flciently strong to Inducea stress equal to or exceeding the yield-point stress.Since increased airspeed-reduees the gust intensityrequired to develop any given stress, for a given airplanethe frequency of occurrence of the ~itlcal:stress willincrease wtth increasing airspeed and hence the single-gust life will depend upon the actual operating speed.

, Fatigue Hfe

The problem of determining the fatigue lif’eof anaircraft struct~wal member subjected to the randomlyvarying loads caused by atmospheric turbulence may bediscussed in three phases: the interpretation of availa-ble gust-frequency data for fatigue studies, the deter-mination of’the fatigue life of a material under randomatresa varlationa~ and the consideration of the effect ofstress concentrations in structural members. A8 variousmethods of solving each of these three components of’theproblem are available, several methods are discussedbriefly and a procedure is chosen as a basis for thisanalysis. Although the procedure selected:gives reasona-ble values of life expectancy, the present status ofknowledge concerning every part of this problem and theproblem as a whole is such that reliance should be placedonly on the trends and general implications of theresults, not on the absolute magnitudes of fatigue life.

Interpretation of gust data.- The determination ofthe s%ress associated with a given effective gust velocityfor the usual assumptions of static loading and uniformdistribution of gust velocity along the span is a well-known process. In spite of their limitations, theseassumptions appear to give reasonably accurate results.(See reference 1.) Tn the present analysis the usualassumptions are therefore retained and the gust inten-sities are converted to stress intensities by using thesimple gust fomula (equation (1) of reference 1).

Fatigue analysis requires the determination of thestresses associated not with a single gust but with manygusts of various magnitudes. Data on the frequency ofoccurrence of gusts of various magnitudes are presentedin reference 1. As shown there, the frequency distri-bution may be represented by the summation curve of therelative-frequency distribution; such a summation curve

.—— —— . -—. ...— . .— -.

4 NACA ARR No. L5F27a

Is reproduced as figure 1 (curve A of fig. 7, reference 1).This curve, together with the Clata”ontotal number ofgusts per mile of operation given in reference 1, providesa basis for the determination of the number of stress “cycles per mile of operation.

A simple and common way of interpreting gust-frequencydata for fatigue studies is to group the gusts in pairsof equal magnitudes having opposite signs for conversionto stress cycles about a constant mean stress correspondingto the lg load on the airplane structure. Unpublishedresults indicate that, actually, only about two-thirds ofthe gusts are grouped In this manner and the other thirdare not. A more nearly correct representation of theother one-third of the data would be effected If the num-ber of cycles for this third were doubled and the rangeof stress reduced to one-half of the range in the simplerrepresentation. The more refined interpretation wouldalso change the mean stress from the values correspondingto lg to a set of values dependent upon the stress ampli-tudes. Examination of fatigue data indicates that thenet effect of the changes introduced by the closerapproximation of the gust d~ta is to increase the esti-mated fatigue life, primarily because of the great effectof the reduction of stress range. The more common inter-pretation, becatlse it is SOm8What more conservative aswell as simpler, has been chosen as a basis for the . -present analysts.

Application of fatigu e data for materials.- Forpractical reasons, fatigue tests of materials are usuallymade in such a way that the fatigue life for a given meanstress is found in terms of the number of stress cyclesrequtred to cause failure with constant amplitude”of thestress cycle. The results of such tests indicate, as 1swell known, that the number of cycles required to causefailure decreases as the stress amplitude or maximumstress increases. The data are usually represented inthe form of S-N curves, an example of which is shown infigure 2. Even in the case of simple specimens ofmaterial, the scatter of the data is so.large that thedetermination of the number of cycles..required to causefailure is accurate only within a factor of 2 or 3 andeven greater factors are not at all uncommon.

Fatigue tests in which the actual nature of stressfluctuations Is precisely represented have not been made,although a few tests have been made In which stress


amplitude has been ohapged on single specimens. Althoughsome general tendencies have been disclosed by these

... teata. the data,are..lnadeauate to.mrnvide a.basis for thepredl~tion of fatigue”stress fluctuations.adding the effects ofrectly, some levelingeffects must be used.

lif% under tbe action of “randma ‘Since there is no known way ofrandom stress fluctuations cor-or averaging method of adding these

One method, which might be called the linear method,”is to assume a straight-line dsmagtngeffect of the cyclesat any stress level. The number of applied cycles at anylevel is divided by the number of cycles required to causefailure at that level to obtain the fractional damagedone. The cumulative effect or damage caused by allstresses is thus the sum of the fractional damages ateach level and, if the sun exceeds 1.0, failure 1s assumedto have occurred. The basic concept of this method seemsre~sonable, but a difficulty arises in making the propercho2ce of stress Interval. The use of too large aninterval will give erroneous “results whereas too smallan interval will result in an excessive smount of compu-tation and a false concept af accuracy. The optimumstress interval is therefore a matter of personal :ud~entand experience. Another deficiency In the linear methodis that It does not accmnt for the effect of stressesbelow the endurance limit. The effects of these lowerstresses may be beneficial and can be taken into accountby means of a modification suggested by Langer (refer-ence 2), In which an average fractional damage or repair1s assigned to each cycle at each level. This procedureis cumbersome and requires far more experimental datathan are now available.

Another method of predicting the fatigue life of amaterial, which might be called the intersect method,Involves the assumption (reference 3) that, for any totalnumber of cycles or any duration of operation, the mate-rial is safe if the smmnation curve of the applied stresscycles remains below the corresponding S-N curve of thematerial (fig. 2). In comparing the smmation andS-N curves, it Is found convenient to hold the mean stressconstant. The fatigue life is found when the stress-cyclesummati?n curve, which shifts to the right with increasingnumber of miles flown, contacts the correspondingS-N curve of the material. The intersect method Involvesthe implication either that the damage line is very closeto the S-N curve for the material considered or.that, in

—— .——. ———.. .

6 ‘“ NACA ARR.No. L5F27a

the region of contact, the net beneficial effect of thestress cycles below any level compensates for the damagingeffect of the higher stress cycles to such an extent thatall the higher stress cycles can be considered to occurat that level. The few appll=”ble test results (rafer-ence 4) indicate that this assumption is reasonable.

The linear method gives somewhat shorter llfe (withinthe limits of scatter o: fatigue-test results) than theintersect method when applied to the stress summationcurve derived from gust-frequency data. Applicablefatigue-test results are too few, however, to permit con-clusions concerning the relative accuracy of the twomethods. Since the intersect method has the advantageof simplicity, this metho”d is utilized in the analysis.

Stress-concentration factors.- S0 long as the maximumstres=s in tensio=and compression are below the elasticlimit, any given stress-concentration factor may beapplied in the customary manner (reference 5). The deter-mi]l.ationof the proper stress-concentration factor, how-evei’,presents some difficulty. ‘,Vhenstresses above theel~.stic limit are consldelted,furthermore, the unloadingeff~ct of plastic action In the region of stress. concen-tration reduces the maximum stress below that given bythe stress-concentration factor.

If the average mean stress in cyclic loading is notzero, the effect of the plastic action is to reduce themean st?ess at the point of stress concentration. Thehypothesis used in this report is that the first cyclewhich causes plastic action results in a lowering of themean stress in the region of stress concentration butthat the entire stress-concentration factor is stilleffective wtth regard to the range of a cycle in thisregion. As an example, if a stress-concentration factorof 3 is present and the average mean stress in the memberis A, the value of the stress at the point of stressconcentration is 3A. If the average stress is nowincreased by B, the stress at the point becomes 3(A + B)under elastic conditions. If the amount 3B is sufficientto cause plastic action, however, the most highly stressedportion will unload to a less highly stressed portion andthe maxhuuu stress wI1l be 3(A + B) - A, where A is theamount of unloading. The material at that point willbehave elastically when the average-stress increment B isremoved; and when the stress at the point of maximumstress concentration decreases. by the corresponding

..—— . ..- .-..

NACA ARR No. L5F27a ?

amount 3B, the mean stress at the point beccxnes 3A - A.,. Subsequently, as.long as no average-stress increment

exceeding B is imparted to’the”rn~ber,”””the-stress cyclesin the region of maximum stress mncentratlon will beacting about the lower mean stress 3A - A.

One way of determining the amount of lowering of themean stress due to plastic actionln the region of stressconcentration would be to.make use of the stress-stratncurve of the material and a relaxation method of compu-tation (references 6 and 7). Such a process would betedious and the result, still in doubt. A simple methodwas therefore sought for calculating the stresses in theplastic re@on. It is well lmown that, for moderatestress concentrations in ductile materials, the stressapproaches uniformity at the ultimate strength. ThiSfact led to Hartmainn’s assumption (reference 8) that thestrese-concentraticm factor decreases linearly from themaxlrnum value at three-fourths the yield strength to avalue of 1 at the uitimate strength. This assumption maybe used in conjunction with the discussion just given oncyclic loading in the plastic region to predict fatiguelife, providiilg the initial stress-concentration factorcaa be determined.

When plastic action Is taken into account, no singlefatigue life can be determined, as can be seen from thefollowing considerations. The limiting stress range ofa mate:ial for any given number of cycles ordinarilydecreases slightly with increasing mean stress.at thelower maen stresses; however, the rate of decrease maybecome quite large at higher mean stresses (reference 9).Thus , since the material at the point of stress concen-tration operates at a relatively high mean stress, pro-vided an Initial cycle has not caused plastic action, thefatigue life is slightly low as compared with the lifecorresponding to the lower mean stress. If the Initial c -cycle has caused plastic action in the material, withresultant reduction of ‘mean stress for subsequent cyclesof iover amplitude, the fatigue life Is somewhat Increasedin accordance with the reduction In mean stress. Insummation, the following assumptions were used concerningplastic action: that plastic flow takes place as expressedby Harlmmnn~s relation, that no plastic flow takes placesubsequent to the first cycle, and that any range ofstress remains constant at the full value of the stress-concentration factor times the average-stress range.

1, — .

. . . . . ---- . .


‘1

Since the fatigue life is affeoted by the order inwhich the larger stresses occur, the fatigue life may beplotted as a function of the first stress encountered, asshown in figure 3. It is assmed for this curve that nostress greater than the first is experienced. The lifeobtained when the first stress encountered Is high enoughto make the mean stress at the point of maximum stressconcentration become zero will be referred to as the‘fmsximum llfeti (point A In fig. 3). From the maximumlife, the fatigue llfe decreases with decreasing firststress because of Increasing mean stress in the region ofstress concentration. A reversal In the curve occurs,however, because of the decreasing stress amplitudes; andthe fatigue llfe approaches infinity as the stressdecreases. The life at the point of reversal is con-sidered the minimum- life. Actually, If a low first stressIs subsequently exceeded, the potential life is Increasedfrom that given by the first mean-stress level towardthat of the new mean-stress level. It may be seen that,for normal gust distribution, the fatigue life must fallbetween these two extremes.

CON171TIONS OF ANALYSIS

Although the analysis is restricted to the wing andtakes account of only the stresses Induced by atmosphericgusts, a considerable number of variables inttluence boththe fatigue life and the single-gust life. In order tokeep the analysis as simple as possible and at the sametime to bring out the important points, those variablesthat affect the fatigue ltie and the single-gust life inthe same ratio are held constant. For example, the sizeand the geometrical configuration of the airplane havebeen found to affect the two lives equally; the analysisis therefore presented for only one size and one con-figuration, although the influence of these variables onthe lives will be evident later. The analysis is mostlyfor only one structural material because, although theeffect of change of material is not negligible, theinfluence of other variables is relatively unaffected bythe material chosen. A check is given, however, for asecond material. Although gust frequency 1s actuallyvariable (reference 1), it Is assumed to be constantbecause the Influence of changes in gust frequency can beeasily evaluated without specific trealment in theanalysis. Variables specifically treated Include

—.- ..— —— —. .

NACA ARR No. L5F27a

structural detail - suoh as stress concentrationstress.-load relation...-.,design.speed, design ~ngand basic design oriterlons.

.Constant Factors

9

-loading,

and c=:~::es::c::~_&~~:::~:::$’:ehypothetical airplane having the wing dimensions of theDouglas DC-3. The important factors governed by thischoice are the mean wing chord, 10.4 feet, and the slopeof the wing llft curve, .4.8.

Material of construction.- It was found desirableto have the S-N CWV= Of the selected material rangefrom static load conditions to a great number of cy61es.Since the fatigue characteristics of the common aluminumalloy 17S-T in the region of high stresses and smallnumbers of cycles had been investigated in reference 10and since additional fatigue data of the usual type wereavailable in reference 11, 17S-T was used as the basicmaterial. Another common aluminum alloy, Z@-T, wasinvestigated sufficientl~ to determine the effect ofchanging to this material.

Gust frequency.- The anal~sis is made for the unitsummation curve of relative gust frequencies (fig. 1).This summation curve is the upper limit of the unitsummation curves of gusts from various sources and,consequently, leads to conservative estimates of bothfatigue life and single-gust life. The absolute gustfrequency used in the analysis, 50/V gusts per mile, wasbased on the data given in reference 1 ang is aboutaverage for normal transport operations (c denotes meanwing

SU ch

‘tiordin ft).—

Variable Factors

Structural details.- Since stress concentrations Infomns as holes, illets, grooves, bends, and surface..

blemishes occur In all struct=es, t~ variation offatigue life with stress-concentration factors from 1to 6 was Investigated. Usual stress-concentration factorsfor well-designed and well-fabricated structures aYewithin this range although the higher values are notprecluded. A typical value in a structure ideal except

Im .— - —

10 .NACA A.RRMO. L5F27a

for stress concentrations is 2.4, and in some examplesthis value Is used as a constant while other quantitiesare varied.

llNonllrlearllloading occurs in structures typical ofnormal construction when one portion of a structure isoverloaded because another partion falls to carry Itsdesign s4hareof the load as a result of improper designor fabrication. As the elastic limit is exceeded, theoverloaded portion of the str-~cturemay be relieved moreand more, with the result that at the higher loads theloadlng tends to become uniform. Consequently, althoughthe fatigue life is greatly affected, the static pro-perties and single-gust life are not materially altered.In order to determine the ma&nltude of the effect onfatigue life, a comparison was made between the idealstructure and one in which such overloading was present.In the structure selected, the overload factor was ~/3 upto the elastic limit, after which the factor was reducedlinearly to a value of unity at the yield point.

Operating conditions.- Although operating conditionsdetermine the ratio of f~lght path In rough air to totalflight path and thereby affect the gust frequency permile of operation, the gust frequency per mile is heldconstant for reasons previously given. The actualoperating speed also has an important effect on both thefatigue life and the single-gust life; a variation ofthis speed in roughest air Is considered in the analysis.

Whereas the airplane Is assumed to be designedstatically to yield with application of a 30-foot-per-second gust at design level-flight speed, the airplaneis assumed to operate normally at a cruising speed of 0.8of the design speed. Inasmuch as good operational prac-tice requlr=s a-reduction In speed–below-the normal-crulslng value when the air Is extremely rough, theinfluence of a reduction in speed from 0.8 to 0.6 ofdesign speed during stretches of extremely rough airdetermined.

thewas

Design conditions.- It was assumed, in general, thatthe a~rplane was designed to yield with application ofan effective gust velocity of 30 feet per second atdesign level-flight speed and that the stress was zeroat zero load factor. The effect of reducing the designgust velocity to 25 feet per second was evaluated for onecondition of design speed and wing loading. For a design

.—, .-,.


for an effecttve gust velo”clty of 30 feet per second, t@”effects of variation in wing loading from 10 to 50 poundsper”square foot and vartatiun In design level-flightspeed from 125 to 425 miles per hour were evaluated.

RESULTS AND DISCUSSION

Effect of Structural Parameters

Stress-concentration factor.- The effect of increasingstress-concentration factor on the fatigue life of a wingstructure ideal except for stress concentrations Is shownin figure 4. The results are given for two materials,17S-T and 2)@-T aluminum alloy, and indicate both themaximum and minimum lives as determined by the mostfavorable and the least favorable sequence of gusts. Asis readily apparent, the fatigue life decreases rapidlywith increasing stress-concentration factor, so thatfairly short life is possible with moderately high valuesof the factor.

The comparison between 17S-T and 2@-T aluminumalloys shown In figure 4 is not Intended as an analysisof the effects of different materials on fatigue strengthbut was made simply as a check to insure that the choiceof one In preference to the other would not seriouslyalter the implications of the general analysis, which hasbeen carried out only for 17S-T. The difference infatigue lives for the two materials Is not large. ThiSresult cannot, of course, be construed to mean that choiceof material generally has no influence on the fatiguelife. The similarity in the results for 17S-T and 2@-Tmaterials might have been expected, because the ratio ofthe fatigue strength to ultimate strength in bothmaterials is about the same. In other words, the higherstrength of 2@-T, which causes increased stress ampli-tudes for the assumed design condlti.ens,is about offsetby an improvement in the fatigue-strength qualities ofthe material. In the case of certain high-strengthalloys, the fatigue life may sometimes be adverselyaffected for two reasons: a reduction In the ratio offatigue strength to ultimate strength and an increasein notch sensitivity.

The stress-concentration factor does not affect thesingle-gust life, which Is shown in figure 4 for the

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12 . NACA ARR No. L5F27a

normal cruising speed of 170 miles per hour and for aspeed reduction to 125 miles per hour In the roughest air.It is well known that moderate stress-concentration fac-tors do not appreciably affect static strength of ductilematerials because of the localized nature of the highstress and because the plastic flow of material In theregion of stress concentration causes more uniformdistribution of stress at the higher loads. Since thesingle-gust loading condition is a Itstatlcllphenomenon,as contrasted with a fatigue phenomenon, the single-gustlife remains constant over a wide range of stress-concentratlon factors.

Nonlinear stress-load relation.- The effect of atyplcal structural imperf’ection resulting from desi~or fabrication is shown in fi~e 5, which also shows theresults given in figure 4 for 17S-T material. The natureof the Imperfection has been described in a previoussection. The considerable shortening of fatigue liferesulting from this Imperfection is clearly evident andcorresponds approximately to the reduction caused bymultiplying the stress-concentration factor by 4/3.

Single-gust life is unaffected by the structuralimperfection because the yield point was assumed to havebeen reached with all the material active. With sometypes of structural imperfection, this assumption wouldnot apply and the single-gust life, as defined on thebasis of yield-point stress, would be slightly affected.In no ordinary case, however, would the ultimate staticstrength of the structure be appreciably affected by thetype of structural imperfection under coi~sideration;hence the single-gust life may be considered to beunaffected.

Effect of Operating Conditions

Reduction of operating speed in roughest air.- Bothfigures 4 and b show that the single-gust life Ismaterially affected by the operating speed. In the caseassumed, the single-gust life corresponding to operat onat a cruising speed of 170 miles per hour is 2.6 x 10imiles, whereas the life corresponding to reduction ofoperating speed to 125 miles pe

ihour when the roughest

air Is encountered is 1.04 x 10 miles. It should benoted that the reduced speed need be assumed to apply not

—.—. — .-


to the entire operat~.ng life ‘butonly to the relativelysmall ym.t.dqri,i..w,hieghthe roughest air Is encountered.

The ,reductlon of operating speed in the roughest airhas a negligible effect on the fatigue life, because onlythe stresses resulting from tinerelatively few largergusts and f’roma small number of the smaller gusts havebeen diminished. Diminishing the infrequent largestresses on the summation curve (fig. 2) does not influ-ence thg number of cycles of the smaller stresses requiredto cause contact of the summation and S-N curves. Whenthe large stresses are diminished by a reduction of speed,smm of the smaller strssses resulting from the lesssevere gusts encountered during the operations in therolqjhest air will also be diminished. The nmber of lessintense gusts encountered during the short stretches ofthe roughest air, however, is small compared with thetatal number of the less flnten~e ~gustsand the fatiguelife is only very slightly increased by the reduction inoperating speed. This effect has been neglected In theanalysis. )

Variations in gust frequency.- As pointed out inraference 1 the tgtal frequsficy of significant gasts maybe defined ~n term of the path ratio, which is the ratioof the flight path in rough air to the total path ofoperations. The value of 50/E Eusts per mile chosen forthe present analysis corresponds to & path ratio ofapproxl.uately 0.1, w~ch is t’fl~ rne~ value f’or a number

of different operating mnriitions. The data of refer-ence 1 indicat6 that the path ratio may vary betweenvalues of 0.006 and O.~ according to the operating con-ditions. The fatigue lives shown In the results presentedhere may therefore be multiplied by appropriate factorsto determine the fatig~e lives corresponding to operatingconditions other than average. Similarly, the path ratiohas a direct effect on the single-gust l~fe.

Effect of Trends in Design and Reduction

of Design Gust Velocity

marks%%%$%.- Because wing loading has shown ao tncrease with the development of new

designs, there has been some fear that the correspondingincrease in the mean-stress level would result inshortening the fatigue life. Ii’the design load factor

.

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4 NACA ARR NO. L5F27a

is based on an effective gust velocity of 30 feet persecond, however, there is an offsetting influence in thatthe stress amplitudes are reduced for a given set of gustIntensities.

The net effect on fatigue life and single-gust lifeof change In wing loading when the design is based on aneffective

tust velocity of 30 feet per second is shown

In figure The maximum and minimum fatigue lives areshown for t~o values of the stress-concentration factor,2.~ and 6.o; the single-gust lives are shown for compari-son. It is evident that the net effect on the fatiguelife of increasing the design,wing loading is favorable, “although the effect is only moderate for the highervalues or stress-concentration factor. This resultindicates that the favorable effect of reduction In stressamplitudes has more than offset the deleterious effect ofthe increase in mean stress. Single-gust life remains.the same at all values of the wing loading.

Another trend in design, which has been cited ascausing a reduction of f~tiguo life, is the trend towardlower design load factors. Although the effect of reduc-tion of load factor has not been evaluated with otherfactors remaining constant, it may be pointed out thatincreasing the wing loading lowers the load factor whenthe design is based on the gust criterion. Consequently,lengthening of fatigue life with increasing wing loadingactually exists notwithstanding rather marked reductionin the load factor. Figure 7 shows the yield-point loadfactors corresponding to the wing loadings of figure 6.The load factor decreases from about 5.7 to 2.3 as thewing loading increases from 10 to 50 pounds per square .foot . Although the reduction in load factor occurs atthe same time as an increase in the wing loading, Itshould be borne in mind that trends in various featuresof design are concurrent rather than separate; hence theresult shown in figure 6 IS probably a fairly accurateindication of the effect of design wing loading on fatiguelife.

V .- The effect on fatigue life of Increasingthe des gn speed is shown in figure 8. The single-gustlife Is not appreciably affected by increasing designspeed, because the design Is assumed to be based on agust criterion. Although fatigue life Is evidentlyadversely affected by increasing speed, the effect isonly moderate. The effect of speed approximately offsets


the favorable effect produced by increasing the wingloading, so that, If the wing loading and speed areIncreased concurrently,’not much change in .f’atlgue.llf.e... ‘occurs.

The fatigue life is given in terms of operatingmiles, the important economic factor, rather than interms of hours of operation. If expressed in hours, thefatigue life would appear to be more adversely affectedby increasing speed.

Airplane size.- Data showing that the total frequencyof significant gusts is inversely proportional to thewing chord are given in reference 1. In accordance withthese data, both t-hesingle-gust life and the fatiguelife may be expected to increase linearly with increasingwing chord.

Reduction of desi n ~st velocit–+ +:- ‘he ‘ffect ‘f areduc~o~ me es gn gust ve oci y .rom 30 feet per

sawrd to 25 feet per second is shown in figure 9. It is

evl~en~ that the %tigue lifo is not greatly reduced bythis change but that the single-gust life is reduced toabout one-eighth of Its original value.

Effect of Other Factors

The results a~ the analysis, although somewhatlimited in scope anG possibly oversimplified, provide abasis for assessing the relative Importance on airplanelife of fatigue and sin@e-gast failures. These resultsmay be better appraised by qualitative consideration ofsmne influences that have been neglected in the analysis.

In flight through turbulent air some dpamic over-stress may be present, especially mar the wing tips.Stress Increments due to such d~amic effects may beabout 10 percent of the stress increments resulting fromstatic-load application. Such incremental stresses maybe introduced into the fatigue analysis by changing theload-stress relation In obtaining the stress summationcurve. General conclusions, however, may be drawn byconsidering figure 9. The change in design gust velocityfrom 30 feet per second to 25 feet per second has thesame effect as a u-percent increment in stresses, Ifthe slight change in mean-stress level Is disregarded.For a 10-percent increment due to dynamic action,

.—...—


therefore, the single-gust llfe would be reduced by afactor of about 4 whereas the fatigue life would bereduced by a factor less than 2; thus the effect ofdynamic response on single-gust life is more pronouncedthan the effect on-fati~e life.

The inclusion in the analysis of stress cyclesresulting frmn ground operation would, on the other hand,adversely affect the fatigue life to some extent withoutaffecting the single-gust life unless the structure weredsmaged in the ground operations. E!othfatigue life andsingle-gust life may therefore be expected to be somewhatless than the values given in the analysis.

The gradual increase in the design allowable stressesfor a material has not been considered in this analysis.Again, however, general conclusions may be drawn fromconsideration of figure 9. The change to a design gustvelocity of 25 feet per second is the same as a 1)+-percentincrease In the design allowable strength at a constantdesi~ gust velocity of 30 feet per second. A reductionof the fatigue life by one-half is associated with thischange. “Thus the design allowable stresses used for amaterial.have an important effect on the fatigue life ofthe structure, and the trend to increased design allowablestresses and more effective utilization of a materialwill Iead to reduced fatigue life.

It has been shown that, on the basis of the assump-tions made, the fatigue life is affected by the order ofstressing, and, if t~lefirst stress of a number of cyclesis high, the fatigue life is appreciably increased. Thisresult suggests.that beneficial effe@s might be had byprestressing the fabricated structure.

Comparison of Fatigue, Single-Gust, and Operating Lives

The absolute values of the fatigue and single-gustlives arrived at in this analysis may not be regarded asaccurately established, as previously noted. It iS Ofinterest, nevertheless, to compare the values of lifeexpectancy obtained in the analysis with the m=imumoparating lives of existing airplanes. Specific data onthis subject are no: available, although some informationindicates that commercial transport airplanes operateregularly as much as 8 hours a day over the period oftheir useful lives. If a cruising speed of 170 miles per


hour is assumed, an airplane flown 8 hours a day for10 years.would

Pve an operating life of about 29,000 hours,

or “about 5 x 10 miles: Occasional failures of the over=load t~e and fatigue failures wi.thmoderate values ofstress-concentration factor maybe expected within thislife. ... . .

The fatigue life and single-gust life appear to beof about equal Importance; the actual life Involvlng .either fatigue or direct failure due to overload dependson the Influence of the operating. renditions and thedetail design and construction. A precautionary remarkshould be made, however, regarding any direct comparisonof fatigue and single-gust llves; namely, the fatiguelife applies directly to individual airplanes, whereasthe single-gust life is a value of probability applicableto a considerable number of airplanes of the same type.In other words, before a fatigue failure will occur theindividual airplane must be flown for some length of thebut single-gust failures may occur at any time in the lifeof an airplane.

It should be noted that the occurrence of a fatiguefailure in the primary structure does not necessarilymean catastrophic failure of the structure. Since fatiguefailures occur at points of high stress concentration andmay thus be localized, considerable static strength willnormally remain. Tf the crack caused by fatigie isdetected early, the defective part may be replaced andthe useful llfe,greatly prolonGed. The same opportunitydoes not exist for correcting the effects of singleexcessive gusts except in the Improbable case !n whichthe stress Is carried far enough beyond the elastic limitto cause noticeable permanent set but not far enough tocause complete failure while in the air.

In orderImportance of

CONCLUSIONS

to provide a basis for judging the relativewing failure by fatigue and by single

intense gusts, an-analysis of wing life for-nomalcruising flight was made based on data on the frequencyof atmospheric gusts. The independent variables. con-sidered in the analysis included stress-concentrationfactor, stress-load relation, wing loading, design and

—....-—...-— —— -.. .

. . . .-.

18 NACA ARR No. LsF2’@

cruising” speeds, desi~:~st””ve~ccityy ~d. airplane:aiae.The results indicate that:

1. The fatigue llfe and single-gust life appear tobe of about equal tiportance; the actual life involvlngeither fatigue or direct failure due to overload dependson the influence of the operating conditions and thedetail design and construction.

2. Occasional failures of the overload type andfatigue failures with moderate values of stress-concentration factor may be expected within the operatinglife of some existing airplanes.

3. The trends In design toward higher wing loadlng,reduced load factor, larger size, and Increased speedappear to have a secondary effect on both the fatiguelife and the single-gust life.

~. The design allowable stresses used for a givenmaterial have an important effect on the fatigue ltie ofa structure,and the trend to increased design allowablestresses and more effective utilization of a materialwill lead to reticed fatigue life.

5. Fatigue life is determined primarily by detaildesign and construction and is affected only to a sec-ondary degree by normal changes In operating speed andby moderate changes in design gust velocity.

6. Slngla-gust life is not appreciably affected bythe detail design but is markedly affected by operatingspeed and by changes in design gust velocity.

Langley Memorial Aeronautical LaboratoryNational Advisory Committue for Aeronautics

Langley Field, Va.

EACA ARR No. L5F27a

—...—

19

. REF’EWWCES.

1. Rhode, Richard V., and Donely, Philip:” “Fr’kqu&c~ of”Occurrence of Atmospheric Gusts and of RelatedMads on Alrpiane Structures. NACA ARR NO. I@21,1944.

2. Langer, B. F.: Fatigue Failure from Stress Cycles ofVarying Amplitude. Jour. Appl. Mech., vol. 4,no. 4, DSC. 1937, pp. A-160 - A-162.

3. 131and,Reginald B., and Sandorff, Paul E.: The Con-trol of Life Expectancy in Airplane Structures.Aero. En&. Rev., vol. 2, no. C, Aug. 191+3,pp. 7-21.

4. Gassner, E.: Festigkeitsversuche mit wiederholterBeanspruchung im plu$ze~bau. Luftwissen, M. 6,Nr. 2, Feb. 1939, pp. $1-64.

5. Timoshenko, S. : Strength of Materials. Part II -Advanced Theory and Froblems. D, ‘JanNostrand Co.,Ihc., 1950.

6. l?oX, L., and Soutkwell, R. V.: Relaxation MethodsApplied to Engineering Problems. VIIA. BiharmonicAnalysis as Applied to Flexure and Extension ofFlat Elastic Plates. Ptil. Trans. Roy. SOC.(London), ser. C, vol~ 1, no. 2, Oct. 15, 19~i,PD. 15-56.

7. Christopherson, D. G.: A Theoretical Investigationof Plastic Torsion In an I-deam. Jour. APP1. Mech.,vol. 7, no. 1, March 19)+0,pp. A-1 - A-4.

8. Hartmann, E. C.: Fatigue Test Results. Their Use inDesign Calculations. Produot ~gineering reprint,Feb. 19)+1.

9. SnIth, James 0.: The Effect of Range of Stress onthe Fatigue Strength of Metals. Univ. of Ill.Bull. Na. 334, vol. 39, no. 26, Feb. 194.2.

10. Hartmann, E. C., and Stickley, (1.W.: The Dlreot-Stress Fatigue Strength of 17S-T Aluminum Alloythroughout the Range fratn1/2 to 500,000,000 Cyclesof Stress. NACA TN NO. 865, 1942.

11. Stickley, G. W.: The Fatigue Strengths of SomeWrought Aluminum Alloys. J!JACARB, June 1942.

NACA ARR No. L5F27a Fig. 1

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NATIONAL ADVISORY

COMMITTEE F~ AERONAUTICS1

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Figure 3.- Variationof fatigue life with average first stressin structurefor a stress-concentrationfactor of 2.4.Material, 17S-T aluminumalloy; wing loading, 24.3 poundsper square foot; cruising speed, 170 rnllesper hour.

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NATIONAL ‘ADVISORY

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Figure 4.- Effect of stress-concentration factor and materialof construction on fatigue life. Assumed wing structuredesigned to yield with guet veloclty of 30 feet per eecondat 213 miles per hour; airplsne assumed to operate atcruieing speed of 170 miles per hour.


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I I I COMMITTEE FOAAEROMAU

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F1.gure 5.- Effect on fatigue llfe of a nonllnea? stress-loadrelatlon. Assumed wing structure designed to yield withgust velocity of 30 feetper second at 213 miles per hour;airplane aeauaed to operate at cruising speed of 170 milesPer hour. (Material, 179-T aluminum alloy.)

,...-..— . . .. . .-——..__

Fig. 6 NACA ARR No. L5F2’?a

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-Single-gust life fff170m@.—— —.——— ——— —— ..—— — ——— _f%x. jife

f7if9.life u. u

NATIONAL ADVISORY

COMMITTEE FORAERONAUTICS

/0 30 50LkvJ”wing iooding, lb~s~ft

Figure 6.- Effect of design wing loading on fatigue life withtwo stress-concentration factore. Assumed wing structuredesigned to yield with gust veloclty of 30 feet per secondat 213 miles per hour at each value of design wing loading;airplane assumed to operate at cruising speed of 170 milesper hour. (Material, 17S-T aluminum alloy.)

—.—


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NATIONAL ADVISORY

/7COMMITTEE FOR AERONAUTICS

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Figure 7.- Variation of yield-point load factor with designwing loadlng. Assumed wing structure designed to yieldwith gust velocity of 30 feet per second at 213 miles perhour.

Fig. 0 NACA ARR No. L5F27a

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NATIONAL ADVISORY”

COMMITTEE F09 AERONAUTICS1 I

/.70 zag 250 300 350

De~/gn leve/-f/ight peed, mphFigure 8.- Effect of design airspeed on fatigue life with

two stress-coneentratIon factors. Assumed wing structuredesigned to yield with gust velocity of 30 feet per secondat each value of design level-flight speed; airplaneassumed to operate at 0.8 design level-fllght speed.(Material, 17S-T aluminum alloy.)


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NATIONAL ADVISORYCOMMITTEEF~ AERONAUTICS

,* 5 I--/ z 3’ 5 (.7

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Figure 9:- Effect of reduction of design guot velocity onfatigue life with varying stres8-concentration factor.Assumed wing etructure designed to yield with designgust veloclty at z!13miles per hour; airplane assumed to “operate at crulslng speed of 170 miles per hour.(Material, 1.79-Taluminum alloy.)

, ,,,.—- -.

Illlllllllllulr3 117601364870

i!iu’’mnm lunbobt · i!iu’’mnm lunbobt originally issued i july1945 as advtxnce...

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